Altho it doesn't specify it in the description, the assumption is that said spring is hanging vertically,
so the weight of the block = mg is the force that extends the spring a distance = 10 cm.
Hooke's Law: Spring's force (mg) is directly proportional to the extension distance: F = kx
{where F = force, k = spring constant, and x = spring length extension}
F = mg = kx
k = mg/x = 1(9.8)/0.1 = 98 N/m ANS
Altho an energy approach could be used to solve, it is NOT a two term equation of simply SPE = GPE.
The block moves vertically down a distance = x = 0.10 m, BUT it doesn't Free-Fall that distance.
It falls with the force of the spring pulling UP against it's weight. So negative work is done by the spring force on the block.
GPE + Spring Work = 1/2kx²
mgh - Favg • h = 1/2kx² {where h = x = 0.10 m}
Favg = (9.8 + 0)/2 = 4.9 N
9.8(0.10) - 4.9(0.10) = 1/2k(0.10)²
0.49 = (0.5)k(0.01)
k = 98 N/m